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Simplifying 2a2 + -6a + -3 = 0 Reorder the terms: -3 + -6a + 2a2 = 0 Solving -3 + -6a + 2a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + -3a + a2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -3a + 1.5 + a2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -3a + a2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -3a + a2 = 0 + 1.5 -3a + a2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -3a + a2 = 1.5 The a term is -3a. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3a + 2.25 + a2 = 1.5 + 2.25 Reorder the terms: 2.25 + -3a + a2 = 1.5 + 2.25 Combine like terms: 1.5 + 2.25 = 3.75 2.25 + -3a + a2 = 3.75 Factor a perfect square on the left side: (a + -1.5)(a + -1.5) = 3.75 Calculate the square root of the right side: 1.936491673 Break this problem into two subproblems by setting (a + -1.5) equal to 1.936491673 and -1.936491673.Subproblem 1
a + -1.5 = 1.936491673 Simplifying a + -1.5 = 1.936491673 Reorder the terms: -1.5 + a = 1.936491673 Solving -1.5 + a = 1.936491673 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + a = 1.936491673 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a = 1.936491673 + 1.5 a = 1.936491673 + 1.5 Combine like terms: 1.936491673 + 1.5 = 3.436491673 a = 3.436491673 Simplifying a = 3.436491673Subproblem 2
a + -1.5 = -1.936491673 Simplifying a + -1.5 = -1.936491673 Reorder the terms: -1.5 + a = -1.936491673 Solving -1.5 + a = -1.936491673 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + a = -1.936491673 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a = -1.936491673 + 1.5 a = -1.936491673 + 1.5 Combine like terms: -1.936491673 + 1.5 = -0.436491673 a = -0.436491673 Simplifying a = -0.436491673Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.436491673, -0.436491673}
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